NV4602 Research Methods for Postgraduate Study
Descriptive Statistics

Outline of lecture
 Purpose of descriptive statistics
 Describing categorical variables
 Frequency analysis

 Describing continuous variables
 Summary statistics
 Measures of central tendency, variability and normality

 Normal distribution

 Relevant SPSS commands:
 Descriptives, Compare means, Histograms, Explore
 Next lab session

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Objectives for today
 Understand the importance of exploring the characteristics of your data before conducting the final analyses
 Appreciate why categorical and continuous data require different kinds of descriptive analysis  Identify and define key measures of:
 Central tendency, Variability, Normality

 Explore these data characteristics using various SPSS commands (next lab session) lbic.navitas.com navitas.com

Population and Sample
 Population
 A group of people: e.g. all students at Brunel, all employees in
Company A, all customers
 A set of objects: e.g. all cars produced by Company A in 2012
 Census
 When data is gathered from the whole population
 Sample
 Subset of the population
 Constraints
 Time
 Money
 Availability of researchers lbic.navitas.com 4

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Why do descriptive statistics?
 What do we need to do before we run statistical tests that will provide conclusive answers to our research questions?
 We need to get to know our data better
 A summary or overview

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 What do descriptive statistics allow us to do?
 Describe the general characteristics of the sample from which the data was collected (sample/group sizes, mean age etc.)
 Check variables for violations in the assumptions underlying the statistical tests you intend navitas.com to use

Categorical variables
 Examples of categorical variables?


Gender, nationality, marital status, grade, education level

 Level of measurement?


Nominal and ordinal

 It is usually valuable to know how many cases belong to each group as defined by your categorical variables 

How many cases are there in each category group?

 Most statistical tests require



roughly equal numbers of cases in each group at least 10 cases (but more = better) in all groups

 ...in order to produce reliable results lbic.navitas.com navitas.com

Categorical variables
 Example research questions:


“Is the Product easy to use, attractive, etc?”, “Is website A better than website B?”, “Does working from home decrease productivity”, “Does stress increase customer defection?”

 What was the relative proportion of males and females in your sample?



Demographic information is normally reported in the method section of your report
For e.g. If this is not 50/50 then is the sample representative of the population of interest?

 You may need to collect more data



If the sample does not reflect the demographic structure of the target population
Or is otherwise unbalanced or group sizes are too small for analysis lbic.navitas.com

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Categorical variables
 In SPSS to obtain descriptive statistics for categorical variables, select:
 Analyse > Descriptive
Statistics > Frequencies

Examining the frequency

table for the Gender category variable.

Comparing the groups may be

problematic in this case. Why?

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Categorical variables
 Frequency tables may also be sufficient to fully answer simple questions
 e.g. Running a count on responses to a question:


“Which is your favourite social media platform?”

 Could also provide a rank order of popularity
 But no test of statistical ‘significance’



(simplistic) example: in a sample of 200, 99 males and
101 females said they use Twitter.
So, can we conclude that females use Twitter more than males?  We’ll look at significance testing next session lbic.navitas.com navitas.com

Continuous variables
 Continuous variables are scale level measures
 e.g. Age, weight, height, time, test scores,